# Tutor profile: Aidin B.

## Questions

### Subject: Basic Math

How far out would it reach out if would stack (end-to-end) all the people on Earth on each other?

Currently, there are 7.8 billion people living on Earth. The average height of a person in 165 cm. So, the total length will be: $$7.8 \cdot 10^9 \cdot 1.65 \ m \approx 10^{10} m = 10^7 km$$

### Subject: Physics

What is the gravitational acceleration on Mars?

We can calculate the gravitational acceleration using the Law of Gravity: $$F_G = - \gamma \frac{M_{marse} m}{r^2}$$, where $$\gamma$$ is the gravitational constant. This force is equal to $$-mg_{mars}$$. So, we get: $$g_{mars} = \gamma \frac{M_{marse}}{r^2} $$. Using, the mass of Mars and its radius, we have: $$g_{mars} = 3.7 \frac {m} {s^2}$$

### Subject: Algebra

Why are the solutions to the quadratic equation are what they are (quadratic formula)? How to derive the solution?

Given a quadratic equation in general form: $$ ax^2 + bx+c=0 $$. The idea of the solution is to complete the square. More, precisely if $$a \ne 0$$: $$ax^2 + bx+c=a(x^2 + \frac{b}ax + \frac{c}a ) = a((x + \frac{b}{2a})^2 + \frac{c}a - \frac{b^2}{4a^2} ) = 0 $$. Thus, $$(x + \frac{b}{2a})^2 = -\frac{c}a+ \frac{b^2}{4a^2} \leftrightarrow x = -\frac{b}{2a} \pm \sqrt{\frac{b^2-4ac}{4a^2}}$$. Or, finally: $$x = \frac{-b \pm \sqrt{b^2-4ac}}{2a} $$

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